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Uhhhh-can-you-guys-solve-Partial-differantial-equation-2-0-Cylinderical-Laplacian-case-2-1-1-2-2-2-2-z-2-Spherical-Laplacian-case-2-

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Question Number 213097 by issac last updated on 30/Oct/24
Uhhhh. can you guys solve Partial differantial equation ▽^2 𝛗=0 Cylinderical Laplacian case ▽^2 =(1/ρ)∙((∂ )/∂ρ)(ρ((∂ )/∂ρ))+((1/ρ))^2 (∂^2 /∂φ^2 )+((∂^2 )/∂z^2 ) Spherical Laplacian case ▽^2 =((1/r))^2 ((∂ )/∂r)(r^2 ((∂ )/∂r))+(1/(r^2 sin(θ)))∙((∂ )/∂θ)(sin(θ)((∂ )/∂θ))+(1/(r^2 sin^2 (θ)))∙(∂^2 /∂ϕ^2 )
Uhhhh.canyouguyssolvePartialdifferantialequation▽2ϕ=0CylindericalLaplaciancase▽2=1ρ⋅∂∂ρ(ρ∂∂ρ)+(1ρ)2∂2∂ϕ2+∂2∂z2SphericalLaplaciancase▽2=(1r)2∂∂r(r2∂∂r)+1r2sin(θ)⋅∂∂θ(sin(θ)∂∂θ)+1r2sin2(θ)⋅∂2∂φ2
Answered by MrGaster last updated on 30/Oct/24
▽^2 φ=0 (1/ρ) (∂/∂ρ)(ρ(∂φ/∂φ))+(1/ρ^2 ) (∂^2 φ/∂φ^2 )+(∂^2 φ/∂z^2 )=0 (1/r^2 ) (∂/∂r)(r^2 (∂φ/∂r))+(1/(r^2 sin θ)) (∂/∂θ)(sin θ(∂φ/∂θ))+(1/(r^2 sin^2 θ)) (∂^2 φ/∂ϕ^2 )=0
▽2ϕ=01ρ∂∂ρ(ρ∂ϕ∂ϕ)+1ρ2∂2ϕ∂ϕ2+∂2ϕ∂z2=01r2∂∂r(r2∂ϕ∂r)+1r2sinθ∂∂θ(sinθ∂ϕ∂θ)+1r2sin2θ∂2ϕ∂φ2=0

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